Hi,

You are right, the system relay is picked by a ground from the ECU on that yellow/red wire. The system relay then provides battery power (from the 25A fender mounted fuse) to the ECU and AMM. The only reason the ECU provides the ground for that relay is in order to leave power up for a few seconds after you shut off the ignition, to allow the AMM wire to be heated for burn-off cleaning. Otherwise, supplying your own ground to that wire is a harmless fix.

The other relay is the fuel pump relay, operating both fuel pumps (tank and main) plus supplying the current for the injectors and idle valve. That relay does not pull in with ignition key on, but only pulls in during cranking and running, when the ECU detects pulses at the ignition coil.

It is likely water followed the harness into the relay, so it may have invaded the other relay or the ECU too, though less likely.

Make sure fuse 12 is good and clean. Its voltage is needed on the ECU (a blue/red wire also found on the fuel pump relay) in order to give the system relay its ground.
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Art Benstein near Baltimore

No matter how hard you try, you can't baptize cats.